LMFDB - Embedded newform 529.8.a.j.1.55

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [529,8,Mod(1,529)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(529, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("529.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 529 = 23^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	529.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$165.251678481$
Analytic rank:	$1$
Dimension:	$65$
Twist minimal:	no (minimal twist has level 23)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.55
Character	$\chi$	$=$	529.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+16.3929 q^{2} +83.4847 q^{3} +140.728 q^{4} -338.591 q^{5} +1368.56 q^{6} +736.684 q^{7} +208.646 q^{8} +4782.69 q^{9} +O(q^{10})$	\(q+16.3929 q^{2} +83.4847 q^{3} +140.728 q^{4} -338.591 q^{5} +1368.56 q^{6} +736.684 q^{7} +208.646 q^{8} +4782.69 q^{9} -5550.49 q^{10} -3210.44 q^{11} +11748.6 q^{12} -9074.76 q^{13} +12076.4 q^{14} -28267.1 q^{15} -14592.8 q^{16} -21664.5 q^{17} +78402.2 q^{18} -41497.5 q^{19} -47649.1 q^{20} +61501.8 q^{21} -52628.5 q^{22} +17418.7 q^{24} +36518.7 q^{25} -148762. q^{26} +216700. q^{27} +103672. q^{28} +186237. q^{29} -463381. q^{30} -26969.2 q^{31} -265926. q^{32} -268022. q^{33} -355145. q^{34} -249434. q^{35} +673057. q^{36} -335309. q^{37} -680265. q^{38} -757603. q^{39} -70645.4 q^{40} -282583. q^{41} +1.00819e6 q^{42} -235425. q^{43} -451798. q^{44} -1.61937e6 q^{45} +1.13207e6 q^{47} -1.21828e6 q^{48} -280840. q^{49} +598648. q^{50} -1.80865e6 q^{51} -1.27707e6 q^{52} -72039.4 q^{53} +3.55235e6 q^{54} +1.08702e6 q^{55} +153706. q^{56} -3.46440e6 q^{57} +3.05297e6 q^{58} -1.87957e6 q^{59} -3.97797e6 q^{60} -258.019 q^{61} -442104. q^{62} +3.52333e6 q^{63} -2.49142e6 q^{64} +3.07263e6 q^{65} -4.39367e6 q^{66} +3.36449e6 q^{67} -3.04880e6 q^{68} -4.08896e6 q^{70} +3.80823e6 q^{71} +997887. q^{72} -1.70273e6 q^{73} -5.49670e6 q^{74} +3.04875e6 q^{75} -5.83985e6 q^{76} -2.36508e6 q^{77} -1.24193e7 q^{78} +1.49616e6 q^{79} +4.94100e6 q^{80} +7.63141e6 q^{81} -4.63236e6 q^{82} -8.57869e6 q^{83} +8.65501e6 q^{84} +7.33541e6 q^{85} -3.85931e6 q^{86} +1.55479e7 q^{87} -669844. q^{88} +1.75273e6 q^{89} -2.65463e7 q^{90} -6.68523e6 q^{91} -2.25152e6 q^{93} +1.85579e7 q^{94} +1.40507e7 q^{95} -2.22007e7 q^{96} +3.50274e6 q^{97} -4.60379e6 q^{98} -1.53545e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 65 q + 8 q^{2} + 14 q^{3} + 3776 q^{4} - 1181 q^{5} + 1082 q^{6} - 3628 q^{7} - 5757 q^{8} + 38263 q^{9}+O(q^{10}) $ 65 * q + 8 * q^2 + 14 * q^3 + 3776 * q^4 - 1181 * q^5 + 1082 * q^6 - 3628 * q^7 - 5757 * q^8 + 38263 * q^9	\( 65 q + 8 q^{2} + 14 q^{3} + 3776 q^{4} - 1181 q^{5} + 1082 q^{6} - 3628 q^{7} - 5757 q^{8} + 38263 q^{9} - 6879 q^{10} - 26147 q^{11} + 35689 q^{12} - 100 q^{13} - 55020 q^{14} - 92935 q^{15} + 176888 q^{16} - 89552 q^{17} + 190670 q^{18} - 169530 q^{19} - 210098 q^{20} - 190951 q^{21} - 218663 q^{22} + 190835 q^{24} + 721210 q^{25} + 186894 q^{26} - 670321 q^{27} - 366019 q^{28} + 340963 q^{29} - 671873 q^{30} - 175163 q^{31} - 406068 q^{32} - 726837 q^{33} - 1110895 q^{34} - 596883 q^{35} + 361164 q^{36} - 790283 q^{37} - 1963838 q^{38} - 21993 q^{39} - 1600645 q^{40} - 623859 q^{41} - 2696872 q^{42} - 1189188 q^{43} - 3885217 q^{44} - 2158369 q^{45} + 1365507 q^{47} + 1218748 q^{48} + 5854235 q^{49} - 2728396 q^{50} - 4554663 q^{51} + 7887791 q^{52} - 4362562 q^{53} + 5072916 q^{54} - 3989544 q^{55} - 12949007 q^{56} - 551326 q^{57} - 7443768 q^{58} + 13201460 q^{59} - 19296285 q^{60} - 8838644 q^{61} - 14615728 q^{62} - 12479203 q^{63} - 9711751 q^{64} - 13544545 q^{65} - 4907285 q^{66} - 5760553 q^{67} - 17044359 q^{68} + 6122411 q^{70} + 4531745 q^{71} + 10759455 q^{72} - 2535486 q^{73} - 21404597 q^{74} + 22917428 q^{75} - 21958812 q^{76} + 11733492 q^{77} - 35437508 q^{78} - 27234683 q^{79} - 28932289 q^{80} + 3995985 q^{81} - 11682773 q^{82} - 39797339 q^{83} - 33971997 q^{84} - 19766357 q^{85} - 43836707 q^{86} - 13972389 q^{87} - 33099818 q^{88} - 41235321 q^{89} - 17210275 q^{90} - 30292506 q^{91} + 47965734 q^{93} - 9981701 q^{94} - 5998448 q^{95} - 48738628 q^{96} - 13984256 q^{97} + 56728191 q^{98} - 81303822 q^{99}+O(q^{100}) \) 65 * q + 8 * q^2 + 14 * q^3 + 3776 * q^4 - 1181 * q^5 + 1082 * q^6 - 3628 * q^7 - 5757 * q^8 + 38263 * q^9 - 6879 * q^10 - 26147 * q^11 + 35689 * q^12 - 100 * q^13 - 55020 * q^14 - 92935 * q^15 + 176888 * q^16 - 89552 * q^17 + 190670 * q^18 - 169530 * q^19 - 210098 * q^20 - 190951 * q^21 - 218663 * q^22 + 190835 * q^24 + 721210 * q^25 + 186894 * q^26 - 670321 * q^27 - 366019 * q^28 + 340963 * q^29 - 671873 * q^30 - 175163 * q^31 - 406068 * q^32 - 726837 * q^33 - 1110895 * q^34 - 596883 * q^35 + 361164 * q^36 - 790283 * q^37 - 1963838 * q^38 - 21993 * q^39 - 1600645 * q^40 - 623859 * q^41 - 2696872 * q^42 - 1189188 * q^43 - 3885217 * q^44 - 2158369 * q^45 + 1365507 * q^47 + 1218748 * q^48 + 5854235 * q^49 - 2728396 * q^50 - 4554663 * q^51 + 7887791 * q^52 - 4362562 * q^53 + 5072916 * q^54 - 3989544 * q^55 - 12949007 * q^56 - 551326 * q^57 - 7443768 * q^58 + 13201460 * q^59 - 19296285 * q^60 - 8838644 * q^61 - 14615728 * q^62 - 12479203 * q^63 - 9711751 * q^64 - 13544545 * q^65 - 4907285 * q^66 - 5760553 * q^67 - 17044359 * q^68 + 6122411 * q^70 + 4531745 * q^71 + 10759455 * q^72 - 2535486 * q^73 - 21404597 * q^74 + 22917428 * q^75 - 21958812 * q^76 + 11733492 * q^77 - 35437508 * q^78 - 27234683 * q^79 - 28932289 * q^80 + 3995985 * q^81 - 11682773 * q^82 - 39797339 * q^83 - 33971997 * q^84 - 19766357 * q^85 - 43836707 * q^86 - 13972389 * q^87 - 33099818 * q^88 - 41235321 * q^89 - 17210275 * q^90 - 30292506 * q^91 + 47965734 * q^93 - 9981701 * q^94 - 5998448 * q^95 - 48738628 * q^96 - 13984256 * q^97 + 56728191 * q^98 - 81303822 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	16.3929	1.44894	0.724471	−	0.689305i	$-0.242084\pi$
$2$	16.3929	1.44894	0.724471	+	0.689305i	$0.242084\pi$
$3$	83.4847	1.78518	0.892591	−	0.450868i	$-0.148885\pi$
$3$	83.4847	1.78518	0.892591	+	0.450868i	$0.148885\pi$
$4$	140.728	1.09944
$5$	−338.591	−1.21138	−0.605690	−	0.795701i	$-0.707103\pi$
$5$	−338.591	−1.21138	−0.605690	+	0.795701i	$0.707103\pi$
$6$	1368.56	2.58663
$7$	736.684	0.811779	0.405890	−	0.913922i	$-0.366962\pi$
$7$	736.684	0.811779	0.405890	+	0.913922i	$0.366962\pi$
$8$	208.646	0.144077
$9$	4782.69	2.18687
$10$	−5550.49	−1.75522
$11$	−3210.44	−0.727260	−0.363630	−	0.931543i	$-0.618463\pi$
$11$	−3210.44	−0.727260	−0.363630	+	0.931543i	$0.618463\pi$
$12$	11748.6	1.96269
$13$	−9074.76	−1.14560	−0.572801	−	0.819695i	$-0.694143\pi$
$13$	−9074.76	−1.14560	−0.572801	+	0.819695i	$0.694143\pi$
$14$	12076.4	1.17622
$15$	−28267.1	−2.16253
$16$	−14592.8	−0.890677
$17$	−21664.5	−1.06949	−0.534746	−	0.845013i	$-0.679593\pi$
$17$	−21664.5	−1.06949	−0.534746	+	0.845013i	$0.679593\pi$
$18$	78402.2	3.16865
$19$	−41497.5	−1.38798	−0.693991	−	0.719983i	$-0.744149\pi$
$19$	−41497.5	−1.38798	−0.693991	+	0.719983i	$0.744149\pi$
$20$	−47649.1	−1.33183
$21$	61501.8	1.44917
$22$	−52628.5	−1.05376
$23$	0	0
$23$	0	0
$24$	17418.7	0.257203
$25$	36518.7	0.467440
$26$	−148762.	−1.65991
$27$	216700.	2.11878
$28$	103672.	0.892499
$29$	186237.	1.41799	0.708995	−	0.705213i	$-0.249149\pi$
$29$	186237.	1.41799	0.708995	+	0.705213i	$0.249149\pi$
$30$	−463381.	−3.13338
$31$	−26969.2	−0.162593	−0.0812967	−	0.996690i	$-0.525906\pi$
$31$	−26969.2	−0.162593	−0.0812967	+	0.996690i	$0.525906\pi$
$32$	−265926.	−1.43462
$33$	−268022.	−1.29829
$34$	−355145.	−1.54963
$35$	−249434.	−0.983372
$36$	673057.	2.40433
$37$	−335309.	−1.08828	−0.544139	−	0.838995i	$-0.683143\pi$
$37$	−335309.	−1.08828	−0.544139	+	0.838995i	$0.683143\pi$
$38$	−680265.	−2.01111
$39$	−757603.	−2.04511
$40$	−70645.4	−0.174532
$41$	−282583.	−0.640328	−0.320164	−	0.947362i	$-0.603738\pi$
$41$	−282583.	−0.640328	−0.320164	+	0.947362i	$0.603738\pi$
$42$	1.00819e6	2.09977
$43$	−235425.	−0.451558	−0.225779	−	0.974179i	$-0.572493\pi$
$43$	−235425.	−0.451558	−0.225779	+	0.974179i	$0.572493\pi$
$44$	−451798.	−0.799576
$45$	−1.61937e6	−2.64913
$46$	0	0
$47$	1.13207e6	1.59049	0.795243	−	0.606291i	$-0.207343\pi$
$47$	1.13207e6	1.59049	0.795243	+	0.606291i	$0.207343\pi$
$48$	−1.21828e6	−1.59002
$49$	−280840.	−0.341015
$50$	598648.	0.677293
$51$	−1.80865e6	−1.90924
$52$	−1.27707e6	−1.25952
$53$	−72039.4	−0.0664667	−0.0332334	−	0.999448i	$-0.510580\pi$
$53$	−72039.4	−0.0664667	−0.0332334	+	0.999448i	$0.510580\pi$
$54$	3.55235e6	3.06999
$55$	1.08702e6	0.880988
$56$	153706.	0.116959
$57$	−3.46440e6	−2.47780
$58$	3.05297e6	2.05459
$59$	−1.87957e6	−1.19145	−0.595726	−	0.803188i	$-0.703136\pi$
$59$	−1.87957e6	−1.19145	−0.595726	+	0.803188i	$0.703136\pi$
$60$	−3.97797e6	−2.37756
$61$	−258.019	−0.000145545 0	−7.27725e−5	−	1.00000i	$-0.500023\pi$
$61$	−258.019	−0.000145545 0	−7.27725e−5		1.00000i	$0.500023\pi$
$62$	−442104.	−0.235588
$63$	3.52333e6	1.77526
$64$	−2.49142e6	−1.18800
$65$	3.07263e6	1.38776
$66$	−4.39367e6	−1.88115
$67$	3.36449e6	1.36665	0.683325	−	0.730114i	$-0.260533\pi$
$67$	3.36449e6	1.36665	0.683325	+	0.730114i	$0.260533\pi$
$68$	−3.04880e6	−1.17584
$69$	0	0
$70$	−4.08896e6	−1.42485
$71$	3.80823e6	1.26276	0.631378	−	0.775475i	$-0.282490\pi$
$71$	3.80823e6	1.26276	0.631378	+	0.775475i	$0.282490\pi$
$72$	997887.	0.315078
$73$	−1.70273e6	−0.512291	−0.256145	−	0.966638i	$-0.582453\pi$
$73$	−1.70273e6	−0.512291	−0.256145	+	0.966638i	$0.582453\pi$
$74$	−5.49670e6	−1.57685
$75$	3.04875e6	0.834465
$76$	−5.83985e6	−1.52600
$77$	−2.36508e6	−0.590375
$78$	−1.24193e7	−2.96324
$79$	1.49616e6	0.341415	0.170707	−	0.985322i	$-0.445395\pi$
$79$	1.49616e6	0.341415	0.170707	+	0.985322i	$0.445395\pi$
$80$	4.94100e6	1.07895
$81$	7.63141e6	1.59554
$82$	−4.63236e6	−0.927799
$83$	−8.57869e6	−1.64683	−0.823413	−	0.567443i	$-0.807933\pi$
$83$	−8.57869e6	−1.64683	−0.823413	+	0.567443i	$0.807933\pi$
$84$	8.65501e6	1.59327
$85$	7.33541e6	1.29556
$86$	−3.85931e6	−0.654282
$87$	1.55479e7	2.53137
$88$	−669844.	−0.104781
$89$	1.75273e6	0.263542	0.131771	−	0.991280i	$-0.457934\pi$
$89$	1.75273e6	0.263542	0.131771	+	0.991280i	$0.457934\pi$
$90$	−2.65463e7	−3.83844
$91$	−6.68523e6	−0.929975
$92$	0	0
$93$	−2.25152e6	−0.290259
$94$	1.85579e7	2.30452
$95$	1.40507e7	1.68137
$96$	−2.22007e7	−2.56105
$97$	3.50274e6	0.389678	0.194839	−	0.980835i	$-0.437581\pi$
$97$	3.50274e6	0.389678	0.194839	+	0.980835i	$0.437581\pi$
$98$	−4.60379e6	−0.494111
$99$	−1.53545e7	−1.59043
$100$	5.13920e6	0.513920
$101$	−1.01898e6	−0.0984104	−0.0492052	−	0.998789i	$-0.515669\pi$
$101$	−1.01898e6	−0.0984104	−0.0492052	+	0.998789i	$0.515669\pi$
$102$	−2.96491e7	−2.76638
$103$	1.07208e7	0.966713	0.483356	−	0.875424i	$-0.339418\pi$
$103$	1.07208e7	0.966713	0.483356	+	0.875424i	$0.339418\pi$
$104$	−1.89341e6	−0.165055
$105$	−2.08239e7	−1.75550
$106$	−1.18094e6	−0.0963065
$107$	1.11949e7	0.883440	0.441720	−	0.897153i	$-0.354368\pi$
$107$	1.11949e7	0.883440	0.441720	+	0.897153i	$0.354368\pi$
$108$	3.04958e7	2.32946
$109$	1.30249e7	0.963344	0.481672	−	0.876352i	$-0.340030\pi$
$109$	1.30249e7	0.963344	0.481672	+	0.876352i	$0.340030\pi$
$110$	1.78195e7	1.27650
$111$	−2.79932e7	−1.94277
$112$	−1.07503e7	−0.723033
$113$	−1.30597e7	−0.851451	−0.425725	−	0.904852i	$-0.639981\pi$
$113$	−1.30597e7	−0.851451	−0.425725	+	0.904852i	$0.639981\pi$
$114$	−5.67917e7	−3.59019
$115$	0	0
$116$	2.62087e7	1.55899
$117$	−4.34018e7	−2.50528
$118$	−3.08117e7	−1.72635
$119$	−1.59599e7	−0.868192
$120$	−5.89781e6	−0.311571
$121$	−9.18026e6	−0.471092
$122$	−4229.69	−0.000210886 0
$123$	−2.35913e7	−1.14310
$124$	−3.79532e6	−0.178761
$125$	1.40875e7	0.645133
$126$	5.77576e7	2.57225
$127$	−769876.	−0.0333509	−0.0166755	−	0.999861i	$-0.505308\pi$
$127$	−769876.	−0.0333509	−0.0166755	+	0.999861i	$0.505308\pi$
$128$	−6.80310e6	−0.286729
$129$	−1.96544e7	−0.806113
$130$	5.03694e7	2.01078
$131$	−2.76562e7	−1.07484	−0.537419	−	0.843315i	$-0.680601\pi$
$131$	−2.76562e7	−1.07484	−0.537419	+	0.843315i	$0.680601\pi$
$132$	−3.77182e7	−1.42739
$133$	−3.05705e7	−1.12674
$134$	5.51538e7	1.98020
$135$	−7.33727e7	−2.56665
$136$	−4.52020e6	−0.154089
$137$	2.71467e7	0.901977	0.450988	−	0.892530i	$-0.351072\pi$
$137$	2.71467e7	0.901977	0.450988	+	0.892530i	$0.351072\pi$
$138$	0	0
$139$	5.58689e6	0.176449	0.0882243	−	0.996101i	$-0.471881\pi$
$139$	5.58689e6	0.176449	0.0882243	+	0.996101i	$0.471881\pi$
$140$	−3.51023e7	−1.08115
$141$	9.45103e7	2.83931
$142$	6.24280e7	1.82966
$143$	2.91340e7	0.833150
$144$	−6.97931e7	−1.94780
$145$	−6.30582e7	−1.71772
$146$	−2.79128e7	−0.742280
$147$	−2.34459e7	−0.608773
$148$	−4.71873e7	−1.19649
$149$	−3.74459e7	−0.927368	−0.463684	−	0.886001i	$-0.653473\pi$
$149$	−3.74459e7	−0.927368	−0.463684	+	0.886001i	$0.653473\pi$
$150$	4.99780e7	1.20909
$151$	−7.41132e7	−1.75177	−0.875883	−	0.482523i	$-0.839721\pi$
$151$	−7.41132e7	−1.75177	−0.875883	+	0.482523i	$0.839721\pi$
$152$	−8.65826e6	−0.199976
$153$	−1.03615e8	−2.33884
$154$	−3.87705e7	−0.855419
$155$	9.13153e6	0.196962
$156$	−1.06616e8	−2.24846
$157$	−1.54008e7	−0.317610	−0.158805	−	0.987310i	$-0.550764\pi$
$157$	−1.54008e7	−0.317610	−0.158805	+	0.987310i	$0.550764\pi$
$158$	2.45264e7	0.494691
$159$	−6.01418e6	−0.118655
$160$	9.00401e7	1.73786
$161$	0	0
$162$	1.25101e8	2.31184
$163$	−2.40562e7	−0.435081	−0.217540	−	0.976051i	$-0.569803\pi$
$163$	−2.40562e7	−0.435081	−0.217540	+	0.976051i	$0.569803\pi$
$164$	−3.97673e7	−0.703999
$165$	9.07499e7	1.57272
$166$	−1.40630e8	−2.38616
$167$	−8.90659e7	−1.47980	−0.739901	−	0.672715i	$-0.765128\pi$
$167$	−8.90659e7	−1.47980	−0.739901	+	0.672715i	$0.765128\pi$
$168$	1.28321e7	0.208792
$169$	1.96028e7	0.312402
$170$	1.20249e8	1.87719
$171$	−1.98470e8	−3.03534
$172$	−3.31309e7	−0.496459
$173$	4.46616e7	0.655802	0.327901	−	0.944712i	$-0.393659\pi$
$173$	4.46616e7	0.655802	0.327901	+	0.944712i	$0.393659\pi$
$174$	2.54876e8	3.66781
$175$	2.69027e7	0.379458
$176$	4.68494e7	0.647754
$177$	−1.56915e8	−2.12696
$178$	2.87324e7	0.381857
$179$	5.91332e7	0.770629	0.385315	−	0.922785i	$-0.374093\pi$
$179$	5.91332e7	0.770629	0.385315	+	0.922785i	$0.374093\pi$
$180$	−2.27891e8	−2.91255
$181$	1.97550e7	0.247630	0.123815	−	0.992305i	$-0.460487\pi$
$181$	1.97550e7	0.247630	0.123815	+	0.992305i	$0.460487\pi$
$182$	−1.09590e8	−1.34748
$183$	−21540.6	−0.000259824 0
$184$	0	0
$185$	1.13533e8	1.31832
$186$	−3.69089e7	−0.420568
$187$	6.95526e7	0.777800
$188$	1.59313e8	1.74864
$189$	1.59640e8	1.71998
$190$	2.30331e8	2.43621
$191$	6.95746e7	0.722494	0.361247	−	0.932470i	$-0.382351\pi$
$191$	6.95746e7	0.722494	0.361247	+	0.932470i	$0.382351\pi$
$192$	−2.07995e8	−2.12080
$193$	−3.80027e6	−0.0380508	−0.0190254	−	0.999819i	$-0.506056\pi$
$193$	−3.80027e6	−0.0380508	−0.0190254	+	0.999819i	$0.506056\pi$
$194$	5.74201e7	0.564622
$195$	2.56518e8	2.47740
$196$	−3.95220e7	−0.374924
$197$	−5.64335e7	−0.525902	−0.262951	−	0.964809i	$-0.584696\pi$
$197$	−5.64335e7	−0.525902	−0.262951	+	0.964809i	$0.584696\pi$
$198$	−2.51706e8	−2.30444
$199$	1.36312e6	0.0122617	0.00613083	−	0.999981i	$-0.498048\pi$
$199$	1.36312e6	0.0122617	0.00613083	+	0.999981i	$0.498048\pi$
$200$	7.61947e6	0.0673472
$201$	2.80883e8	2.43972
$202$	−1.67041e7	−0.142591
$203$	1.37198e8	1.15109
$204$	−2.54528e8	−2.09908
$205$	9.56800e7	0.775680
$206$	1.75745e8	1.40071
$207$	0	0
$208$	1.32427e8	1.02036
$209$	1.33225e8	1.00942
$210$	−3.41365e8	−2.54362
$211$	−1.15332e8	−0.845207	−0.422603	−	0.906315i	$-0.638884\pi$
$211$	−1.15332e8	−0.845207	−0.422603	+	0.906315i	$0.638884\pi$
$212$	−1.01379e7	−0.0730759
$213$	3.17929e8	2.25425
$214$	1.83517e8	1.28005
$215$	7.97129e7	0.547008
$216$	4.52135e7	0.305267
$217$	−1.98678e7	−0.131990
$218$	2.13516e8	1.39583
$219$	−1.42152e8	−0.914532
$220$	1.52975e8	0.968590
$221$	1.96600e8	1.22521
$222$	−4.58890e8	−2.81497
$223$	1.40708e7	0.0849670	0.0424835	−	0.999097i	$-0.486473\pi$
$223$	1.40708e7	0.0849670	0.0424835	+	0.999097i	$0.486473\pi$
$224$	−1.95903e8	−1.16459
$225$	1.74658e8	1.02223
$226$	−2.14087e8	−1.23370
$227$	1.13960e8	0.646639	0.323320	−	0.946290i	$-0.395201\pi$
$227$	1.13960e8	0.646639	0.323320	+	0.946290i	$0.395201\pi$
$228$	−4.87538e8	−2.72418
$229$	1.05245e8	0.579132	0.289566	−	0.957158i	$-0.406489\pi$
$229$	1.05245e8	0.579132	0.289566	+	0.957158i	$0.406489\pi$
$230$	0	0
$231$	−1.97448e8	−1.05393
$232$	3.88575e7	0.204299
$233$	8.52263e7	0.441395	0.220698	−	0.975342i	$-0.429167\pi$
$233$	8.52263e7	0.441395	0.220698	+	0.975342i	$0.429167\pi$
$234$	−7.11482e8	−3.63001
$235$	−3.83308e8	−1.92668
$236$	−2.64508e8	−1.30993
$237$	1.24906e8	0.609487
$238$	−2.61629e8	−1.25796
$239$	1.65538e6	0.00784344	0.00392172	−	0.999992i	$-0.498752\pi$
$239$	1.65538e6	0.00784344	0.00392172	+	0.999992i	$0.498752\pi$
$240$	4.12498e8	1.92612
$241$	−1.95902e8	−0.901530	−0.450765	−	0.892643i	$-0.648849\pi$
$241$	−1.95902e8	−0.901530	−0.450765	+	0.892643i	$0.648849\pi$
$242$	−1.50491e8	−0.682586
$243$	1.63182e8	0.729543
$244$	−36310.5	−0.000160017 0
$245$	9.50900e7	0.413098
$246$	−3.86731e8	−1.65629
$247$	3.76580e8	1.59007
$248$	−5.62701e6	−0.0234259
$249$	−7.16189e8	−2.93988
$250$	2.30935e8	0.934760
$251$	2.55891e8	1.02140	0.510701	−	0.859758i	$-0.329386\pi$
$251$	2.55891e8	1.02140	0.510701	+	0.859758i	$0.329386\pi$
$252$	4.95830e8	1.95178
$253$	0	0
$254$	−1.26205e7	−0.0483236
$255$	6.12394e8	2.31281
$256$	2.07379e8	0.772547
$257$	−4.54892e8	−1.67164	−0.835819	−	0.549005i	$-0.815007\pi$
$257$	−4.54892e8	−1.67164	−0.835819	+	0.549005i	$0.815007\pi$
$258$	−3.22193e8	−1.16801
$259$	−2.47017e8	−0.883441
$260$	4.32405e8	1.52575
$261$	8.90714e8	3.10096
$262$	−4.53366e8	−1.55738
$263$	−4.08065e8	−1.38320	−0.691600	−	0.722281i	$-0.743094\pi$
$263$	−4.08065e8	−1.38320	−0.691600	+	0.722281i	$0.743094\pi$
$264$	−5.59217e7	−0.187054
$265$	2.43919e7	0.0805164
$266$	−5.01140e8	−1.63258
$267$	1.46326e8	0.470470
$268$	4.73477e8	1.50254
$269$	1.38988e7	0.0435356	0.0217678	−	0.999763i	$-0.493071\pi$
$269$	1.38988e7	0.0435356	0.0217678	+	0.999763i	$0.493071\pi$
$270$	−1.20279e9	−3.71893
$271$	−6.47803e8	−1.97720	−0.988600	−	0.150568i	$-0.951890\pi$
$271$	−6.47803e8	−1.97720	−0.988600	+	0.150568i	$0.951890\pi$
$272$	3.16147e8	0.952572
$273$	−5.58114e8	−1.66017
$274$	4.45014e8	1.30691
$275$	−1.17241e8	−0.339950
$276$	0	0
$277$	−1.55887e7	−0.0440688	−0.0220344	−	0.999757i	$-0.507014\pi$
$277$	−1.55887e7	−0.0440688	−0.0220344	+	0.999757i	$0.507014\pi$
$278$	9.15854e7	0.255664
$279$	−1.28985e8	−0.355571
$280$	−5.20433e7	−0.141681
$281$	−5.18521e7	−0.139410	−0.0697050	−	0.997568i	$-0.522206\pi$
$281$	−5.18521e7	−0.139410	−0.0697050	+	0.997568i	$0.522206\pi$
$282$	1.54930e9	4.11399
$283$	−1.08344e8	−0.284152	−0.142076	−	0.989856i	$-0.545378\pi$
$283$	−1.08344e8	−0.284152	−0.142076	+	0.989856i	$0.545378\pi$
$284$	5.35924e8	1.38832
$285$	1.17301e9	3.00156
$286$	4.77591e8	1.20719
$287$	−2.08174e8	−0.519805
$288$	−1.27184e9	−3.13732
$289$	5.90126e7	0.143814
$290$	−1.03371e9	−2.48888
$291$	2.92425e8	0.695647
$292$	−2.39622e8	−0.563231
$293$	−5.11610e8	−1.18824	−0.594118	−	0.804378i	$-0.702499\pi$
$293$	−5.11610e8	−1.18824	−0.594118	+	0.804378i	$0.702499\pi$
$294$	−3.84346e8	−0.882078
$295$	6.36405e8	1.44330
$296$	−6.99608e7	−0.156796
$297$	−6.95703e8	−1.54091
$298$	−6.13847e8	−1.34370
$299$	0	0
$300$	4.29044e8	0.917440
$301$	−1.73434e8	−0.366566
$302$	−1.21493e9	−2.53821
$303$	−8.50692e7	−0.175680
$304$	6.05566e8	1.23624
$305$	87362.9	0.000176310 0
$306$	−1.69855e9	−3.38885
$307$	5.64382e8	1.11324	0.556620	−	0.830767i	$-0.312098\pi$
$307$	5.64382e8	1.11324	0.556620	+	0.830767i	$0.312098\pi$
$308$	−3.32832e8	−0.649079
$309$	8.95024e8	1.72576
$310$	1.49693e8	0.285387
$311$	1.90079e8	0.358321	0.179161	−	0.983820i	$-0.442662\pi$
$311$	1.90079e8	0.358321	0.179161	+	0.983820i	$0.442662\pi$
$312$	−1.58071e8	−0.294652
$313$	4.22148e8	0.778143	0.389071	−	0.921208i	$-0.372796\pi$
$313$	4.22148e8	0.778143	0.389071	+	0.921208i	$0.372796\pi$
$314$	−2.52464e8	−0.460198
$315$	−1.19297e9	−2.15051
$316$	2.10551e8	0.375364
$317$	5.33001e8	0.939768	0.469884	−	0.882728i	$-0.344296\pi$
$317$	5.33001e8	0.939768	0.469884	+	0.882728i	$0.344296\pi$
$318$	−9.85900e7	−0.171925
$319$	−5.97903e8	−1.03125
$320$	8.43571e8	1.43912
$321$	9.34603e8	1.57710
$322$	0	0
$323$	8.99023e8	1.48444
$324$	1.07395e9	1.75419
$325$	−3.31399e8	−0.535499
$326$	−3.94351e8	−0.630408
$327$	1.08738e9	1.71974
$328$	−5.89597e7	−0.0922564
$329$	8.33975e8	1.29112
$330$	1.48766e9	2.27879
$331$	1.20778e9	1.83059	0.915295	−	0.402784i	$-0.131958\pi$
$331$	1.20778e9	1.83059	0.915295	+	0.402784i	$0.131958\pi$
$332$	−1.20726e9	−1.81058
$333$	−1.60368e9	−2.37992
$334$	−1.46005e9	−2.14415
$335$	−1.13918e9	−1.65553
$336$	−8.97486e8	−1.29074
$337$	−3.38170e8	−0.481316	−0.240658	−	0.970610i	$-0.577363\pi$
$337$	−3.38170e8	−0.481316	−0.240658	+	0.970610i	$0.577363\pi$
$338$	3.21347e8	0.452653
$339$	−1.09029e9	−1.51999
$340$	1.03230e9	1.42439
$341$	8.65831e7	0.118248
$342$	−3.25349e9	−4.39804
$343$	−8.13581e8	−1.08861
$344$	−4.91205e7	−0.0650591
$345$	0	0
$346$	7.32133e8	0.950219
$347$	−3.04174e8	−0.390813	−0.195406	−	0.980722i	$-0.562603\pi$
$347$	−3.04174e8	−0.390813	−0.195406	+	0.980722i	$0.562603\pi$
$348$	2.18803e9	2.78308
$349$	2.67516e8	0.336869	0.168435	−	0.985713i	$-0.446129\pi$
$349$	2.67516e8	0.336869	0.168435	+	0.985713i	$0.446129\pi$
$350$	4.41014e8	0.549813
$351$	−1.96650e9	−2.42728
$352$	8.53739e8	1.04334
$353$	5.64113e8	0.682581	0.341291	−	0.939958i	$-0.389136\pi$
$353$	5.64113e8	0.682581	0.341291	+	0.939958i	$0.389136\pi$
$354$	−2.57230e9	−3.08184
$355$	−1.28943e9	−1.52968
$356$	2.46658e8	0.289748
$357$	−1.33241e9	−1.54988
$358$	9.69365e8	1.11660
$359$	−6.17291e8	−0.704141	−0.352071	−	0.935973i	$-0.614522\pi$
$359$	−6.17291e8	−0.704141	−0.352071	+	0.935973i	$0.614522\pi$
$360$	−3.37875e8	−0.381678
$361$	8.28169e8	0.926496
$362$	3.23843e8	0.358801
$363$	−7.66411e8	−0.840985
$364$	−9.40797e8	−1.02245
$365$	5.76530e8	0.620578
$366$	−353114.	−0.000376471 0
$367$	−1.21530e9	−1.28337	−0.641687	−	0.766966i	$-0.721765\pi$
$367$	−1.21530e9	−1.28337	−0.641687	+	0.766966i	$0.721765\pi$
$368$	0	0
$369$	−1.35151e9	−1.40032
$370$	1.86113e9	1.91017
$371$	−5.30702e7	−0.0539563
$372$	−3.16851e8	−0.319121
$373$	−1.21138e9	−1.20865	−0.604325	−	0.796738i	$-0.706557\pi$
$373$	−1.21138e9	−1.20865	−0.604325	+	0.796738i	$0.706557\pi$
$374$	1.14017e9	1.12699
$375$	1.17609e9	1.15168
$376$	2.36201e8	0.229152
$377$	−1.69006e9	−1.62445
$378$	2.61696e9	2.49216
$379$	1.05619e9	0.996565	0.498283	−	0.867015i	$-0.333964\pi$
$379$	1.05619e9	0.996565	0.498283	+	0.867015i	$0.333964\pi$
$380$	1.97732e9	1.84856
$381$	−6.42728e7	−0.0595374
$382$	1.14053e9	1.04685
$383$	−3.69197e8	−0.335786	−0.167893	−	0.985805i	$-0.553696\pi$
$383$	−3.69197e8	−0.335786	−0.167893	+	0.985805i	$0.553696\pi$
$384$	−5.67954e8	−0.511863
$385$	8.00793e8	0.715168
$386$	−6.22975e7	−0.0551335
$387$	−1.12597e9	−0.987500
$388$	4.92932e8	0.428426
$389$	−8.75745e8	−0.754317	−0.377159	−	0.926149i	$-0.623099\pi$
$389$	−8.75745e8	−0.754317	−0.377159	+	0.926149i	$0.623099\pi$
$390$	4.20507e9	3.58961
$391$	0	0
$392$	−5.85961e7	−0.0491323
$393$	−2.30887e9	−1.91878
$394$	−9.25109e8	−0.762002
$395$	−5.06585e8	−0.413583
$396$	−2.16081e9	−1.74857
$397$	1.89164e9	1.51730	0.758648	−	0.651500i	$-0.225860\pi$
$397$	1.89164e9	1.51730	0.758648	+	0.651500i	$0.225860\pi$
$398$	2.23456e7	0.0177665
$399$	−2.55217e9	−2.01143
$400$	−5.32912e8	−0.416338
$401$	2.07582e9	1.60763	0.803813	−	0.594882i	$-0.202801\pi$
$401$	2.07582e9	1.60763	0.803813	+	0.594882i	$0.202801\pi$
$402$	4.60450e9	3.53501
$403$	2.44739e8	0.186267
$404$	−1.43399e8	−0.108196
$405$	−2.58392e9	−1.93280
$406$	2.24907e9	1.66787
$407$	1.07649e9	0.791461
$408$	−3.77368e8	−0.275077
$409$	2.40073e9	1.73505	0.867524	−	0.497396i	$-0.165710\pi$
$409$	2.40073e9	1.73505	0.867524	+	0.497396i	$0.165710\pi$
$410$	1.56847e9	1.12392
$411$	2.26633e9	1.61019
$412$	1.50872e9	1.06284
$413$	−1.38465e9	−0.967196
$414$	0	0
$415$	2.90466e9	1.99493
$416$	2.41321e9	1.64350
$417$	4.66420e8	0.314993
$418$	2.18395e9	1.46260
$419$	−2.28736e9	−1.51910	−0.759549	−	0.650451i	$-0.774580\pi$
$419$	−2.28736e9	−1.51910	−0.759549	+	0.650451i	$0.774580\pi$
$420$	−2.93051e9	−1.93006
$421$	2.54375e9	1.66145	0.830724	−	0.556684i	$-0.187927\pi$
$421$	2.54375e9	1.66145	0.830724	+	0.556684i	$0.187927\pi$
$422$	−1.89064e9	−1.22466
$423$	5.41433e9	3.47819
$424$	−1.50307e7	−0.00957632
$425$	−7.91160e8	−0.499923
$426$	5.21178e9	3.26628
$427$	−190078.	−0.000118150 0
$428$	1.57543e9	0.971286
$429$	2.43224e9	1.48732
$430$	1.30673e9	0.792584
$431$	2.76344e9	1.66257	0.831284	−	0.555848i	$-0.187607\pi$
$431$	2.76344e9	1.66257	0.831284	+	0.555848i	$0.187607\pi$
$432$	−3.16227e9	−1.88715
$433$	−2.67047e9	−1.58081	−0.790406	−	0.612583i	$-0.790130\pi$
$433$	−2.67047e9	−1.58081	−0.790406	+	0.612583i	$0.790130\pi$
$434$	−3.25691e8	−0.191246
$435$	−5.26439e9	−3.06645
$436$	1.83296e9	1.05913
$437$	0	0
$438$	−2.33029e9	−1.32510
$439$	−2.54512e9	−1.43576	−0.717880	−	0.696167i	$-0.754887\pi$
$439$	−2.54512e9	−1.43576	−0.717880	+	0.696167i	$0.754887\pi$
$440$	2.26803e8	0.126930
$441$	−1.34317e9	−0.745756
$442$	3.22285e9	1.77526
$443$	−3.89455e7	−0.0212835	−0.0106418	−	0.999943i	$-0.503387\pi$
$443$	−3.89455e7	−0.0212835	−0.0106418	+	0.999943i	$0.503387\pi$
$444$	−3.93942e9	−2.13595
$445$	−5.93458e8	−0.319249
$446$	2.30661e8	0.123112
$447$	−3.12616e9	−1.65552
$448$	−1.83539e9	−0.964394
$449$	−2.07530e9	−1.08198	−0.540990	−	0.841029i	$-0.681950\pi$
$449$	−2.07530e9	−1.08198	−0.540990	+	0.841029i	$0.681950\pi$
$450$	2.86315e9	1.48115
$451$	9.07215e8	0.465685
$452$	−1.83787e9	−0.936115
$453$	−6.18732e9	−3.12722
$454$	1.86814e9	0.936943
$455$	2.26356e9	1.12655
$456$	−7.22832e8	−0.356994
$457$	2.06112e9	1.01018	0.505088	−	0.863068i	$-0.331460\pi$
$457$	2.06112e9	1.01018	0.505088	+	0.863068i	$0.331460\pi$
$458$	1.72527e9	0.839129
$459$	−4.69471e9	−2.26602
$460$	0	0
$461$	1.32245e8	0.0628676	0.0314338	−	0.999506i	$-0.489993\pi$
$461$	1.32245e8	0.0628676	0.0314338	+	0.999506i	$0.489993\pi$
$462$	−3.23674e9	−1.52708
$463$	−1.50363e9	−0.704058	−0.352029	−	0.935989i	$-0.614508\pi$
$463$	−1.50363e9	−0.704058	−0.352029	+	0.935989i	$0.614508\pi$
$464$	−2.71773e9	−1.26297
$465$	7.62343e8	0.351613
$466$	1.39711e9	0.639557
$467$	−2.26520e9	−1.02919	−0.514596	−	0.857433i	$-0.672058\pi$
$467$	−2.26520e9	−1.02919	−0.514596	+	0.857433i	$0.672058\pi$
$468$	−6.10783e9	−2.75440
$469$	2.47856e9	1.10942
$470$	−6.28353e9	−2.79165
$471$	−1.28573e9	−0.566991
$472$	−3.92164e8	−0.171661
$473$	7.55819e8	0.328400
$474$	2.04758e9	0.883113
$475$	−1.51543e9	−0.648798
$476$	−2.24600e9	−0.954521
$477$	−3.44542e8	−0.145354
$478$	2.71366e7	0.0113647
$479$	−2.14676e8	−0.0892501	−0.0446251	−	0.999004i	$-0.514209\pi$
$479$	−2.14676e8	−0.0892501	−0.0446251	+	0.999004i	$0.514209\pi$
$480$	7.51697e9	3.10240
$481$	3.04285e9	1.24673
$482$	−3.21141e9	−1.30627
$483$	0	0
$484$	−1.29192e9	−0.517936
$485$	−1.18599e9	−0.472048
$486$	2.67503e9	1.05707
$487$	2.33496e9	0.916069	0.458034	−	0.888935i	$-0.348554\pi$
$487$	2.33496e9	0.916069	0.458034	+	0.888935i	$0.348554\pi$
$488$	−53834.5	−2.09697e−5 0
$489$	−2.00832e9	−0.776698
$490$	1.55880e9	0.598556
$491$	1.35244e9	0.515623	0.257811	−	0.966195i	$-0.416999\pi$
$491$	1.35244e9	0.515623	0.257811	+	0.966195i	$0.416999\pi$
$492$	−3.31996e9	−1.25677
$493$	−4.03474e9	−1.51653
$494$	6.17324e9	2.30393
$495$	5.19890e9	1.92661
$496$	3.93558e8	0.144818
$497$	2.80546e9	1.02508
$498$	−1.17404e10	−4.25972
$499$	3.49248e9	1.25829	0.629147	−	0.777286i	$-0.283404\pi$
$499$	3.49248e9	1.25829	0.629147	+	0.777286i	$0.283404\pi$
$500$	1.98250e9	0.709282
$501$	−7.43564e9	−2.64172
$502$	4.19480e9	1.47995
$503$	−3.47841e9	−1.21869	−0.609345	−	0.792905i	$-0.708567\pi$
$503$	−3.47841e9	−1.21869	−0.609345	+	0.792905i	$0.708567\pi$
$504$	7.35127e8	0.255773
$505$	3.45017e8	0.119212
$506$	0	0
$507$	1.63653e9	0.557695
$508$	−1.08343e8	−0.0366672
$509$	−2.41614e9	−0.812101	−0.406051	−	0.913851i	$-0.633094\pi$
$509$	−2.41614e9	−0.812101	−0.406051	+	0.913851i	$0.633094\pi$
$510$	1.00389e10	3.35113
$511$	−1.25438e9	−0.415867
$512$	4.27034e9	1.40611
$513$	−8.99251e9	−2.94083
$514$	−7.45700e9	−2.42211
$515$	−3.62997e9	−1.17106
$516$	−2.76592e9	−0.886270
$517$	−3.63443e9	−1.15670
$518$	−4.04933e9	−1.28006
$519$	3.72856e9	1.17072
$520$	6.41091e8	0.199944
$521$	4.86999e8	0.150868	0.0754339	−	0.997151i	$-0.475966\pi$
$521$	4.86999e8	0.150868	0.0754339	+	0.997151i	$0.475966\pi$
$522$	1.46014e10	4.49312
$523$	7.85974e8	0.240244	0.120122	−	0.992759i	$-0.461671\pi$
$523$	7.85974e8	0.240244	0.120122	+	0.992759i	$0.461671\pi$
$524$	−3.89199e9	−1.18171
$525$	2.24597e9	0.677401
$526$	−6.68938e9	−2.00418
$527$	5.84275e8	0.173892
$528$	3.91121e9	1.15636
$529$	0	0
$530$	3.99854e8	0.116664
$531$	−8.98940e9	−2.60555
$532$	−4.30212e9	−1.23877
$533$	2.56437e9	0.733560
$534$	2.39871e9	0.681685
$535$	−3.79049e9	−1.07018
$536$	7.01985e8	0.196903
$537$	4.93671e9	1.37571
$538$	2.27842e8	0.0630806
$539$	9.01621e8	0.248007
$540$	−1.03256e10	−2.82187
$541$	−1.83492e9	−0.498228	−0.249114	−	0.968474i	$-0.580139\pi$
$541$	−1.83492e9	−0.498228	−0.249114	+	0.968474i	$0.580139\pi$
$542$	−1.06194e10	−2.86485
$543$	1.64924e9	0.442064
$544$	5.76116e9	1.53431
$545$	−4.41011e9	−1.16697
$546$	−9.14912e9	−2.40550
$547$	1.69712e8	0.0443360	0.0221680	−	0.999754i	$-0.492943\pi$
$547$	1.69712e8	0.0443360	0.0221680	+	0.999754i	$0.492943\pi$
$548$	3.82030e9	0.991665
$549$	−1.23403e6	−0.000318288 0
$550$	−1.92192e9	−0.492569
$551$	−7.72837e9	−1.96815
$552$	0	0
$553$	1.10219e9	0.277153
$554$	−2.55544e8	−0.0638531
$555$	9.47824e9	2.35343
$556$	7.86231e8	0.193994
$557$	−7.57295e8	−0.185683	−0.0928415	−	0.995681i	$-0.529595\pi$
$557$	−7.57295e8	−0.185683	−0.0928415	+	0.995681i	$0.529595\pi$
$558$	−2.11445e9	−0.515202
$559$	2.13643e9	0.517306
$560$	3.63996e9	0.875867
$561$	5.80658e9	1.38851
$562$	−8.50007e8	−0.201997
$563$	5.25817e9	1.24181	0.620905	−	0.783886i	$-0.286765\pi$
$563$	5.25817e9	1.24181	0.620905	+	0.783886i	$0.286765\pi$
$564$	1.33002e10	3.12163
$565$	4.42190e9	1.03143
$566$	−1.77607e9	−0.411720
$567$	5.62193e9	1.29522
$568$	7.94571e8	0.181934
$569$	5.63278e9	1.28183	0.640914	−	0.767612i	$-0.278555\pi$
$569$	5.63278e9	1.28183	0.640914	+	0.767612i	$0.278555\pi$
$570$	1.92291e10	4.34908
$571$	4.15588e9	0.934192	0.467096	−	0.884207i	$-0.345300\pi$
$571$	4.15588e9	0.934192	0.467096	+	0.884207i	$0.345300\pi$
$572$	4.09996e9	0.915995
$573$	5.80842e9	1.28978
$574$	−3.41258e9	−0.753167
$575$	0	0
$576$	−1.19157e10	−2.59801
$577$	5.68728e9	1.23251	0.616253	−	0.787548i	$-0.288650\pi$
$577$	5.68728e9	1.23251	0.616253	+	0.787548i	$0.288650\pi$
$578$	9.67388e8	0.208379
$579$	−3.17264e8	−0.0679276
$580$	−8.87404e9	−1.88853
$581$	−6.31978e9	−1.33686
$582$	4.79370e9	1.00795
$583$	2.31278e8	0.0483386
$584$	−3.55268e8	−0.0738092
$585$	1.46954e10	3.03485
$586$	−8.38679e9	−1.72169
$587$	1.95305e9	0.398548	0.199274	−	0.979944i	$-0.436142\pi$
$587$	1.95305e9	0.398548	0.199274	+	0.979944i	$0.436142\pi$
$588$	−3.29948e9	−0.669307
$589$	1.11916e9	0.225677
$590$	1.04325e10	2.09126
$591$	−4.71133e9	−0.938831
$592$	4.89312e9	0.969303
$593$	−9.14464e9	−1.80084	−0.900420	−	0.435021i	$-0.856741\pi$
$593$	−9.14464e9	−1.80084	−0.900420	+	0.435021i	$0.856741\pi$
$594$	−1.14046e10	−2.23269
$595$	5.40387e9	1.05171
$596$	−5.26968e9	−1.01958
$597$	1.13800e8	0.0218893
$598$	0	0
$599$	−6.48547e9	−1.23296	−0.616478	−	0.787372i	$-0.711441\pi$
$599$	−6.48547e9	−1.23296	−0.616478	+	0.787372i	$0.711441\pi$
$600$	6.36109e8	0.120227
$601$	1.56871e9	0.294769	0.147384	−	0.989079i	$-0.452915\pi$
$601$	1.56871e9	0.294769	0.147384	+	0.989079i	$0.452915\pi$
$602$	−2.84309e9	−0.531133
$603$	1.60913e10	2.98869
$604$	−1.04298e10	−1.92595
$605$	3.10835e9	0.570671
$606$	−1.39453e9	−0.254551
$607$	−1.36381e9	−0.247510	−0.123755	−	0.992313i	$-0.539494\pi$
$607$	−1.36381e9	−0.247510	−0.123755	+	0.992313i	$0.539494\pi$
$608$	1.10353e10	1.99122
$609$	1.14539e10	2.05491
$610$	1.43213e6	0.000255463 0
$611$	−1.02732e10	−1.82206
$612$	−1.45815e10	−2.57141
$613$	4.12622e9	0.723504	0.361752	−	0.932274i	$-0.382179\pi$
$613$	4.12622e9	0.723504	0.361752	+	0.932274i	$0.382179\pi$
$614$	9.25187e9	1.61302
$615$	7.98781e9	1.38473
$616$	−4.93463e8	−0.0850593
$617$	1.01139e10	1.73349	0.866747	−	0.498749i	$-0.166207\pi$
$617$	1.01139e10	1.73349	0.866747	+	0.498749i	$0.166207\pi$
$618$	1.46720e10	2.50052
$619$	−6.33691e9	−1.07389	−0.536946	−	0.843617i	$-0.680422\pi$
$619$	−6.33691e9	−1.07389	−0.536946	+	0.843617i	$0.680422\pi$
$620$	1.28506e9	0.216547
$621$	0	0
$622$	3.11595e9	0.519187
$623$	1.29121e9	0.213938
$624$	1.10556e10	1.82153
$625$	−7.62292e9	−1.24894
$626$	6.92023e9	1.12748
$627$	1.11223e10	1.80201
$628$	−2.16732e9	−0.349191
$629$	7.26431e9	1.16390
$630$	−1.95562e10	−3.11597
$631$	−6.10946e8	−0.0968055	−0.0484027	−	0.998828i	$-0.515413\pi$
$631$	−6.10946e8	−0.0968055	−0.0484027	+	0.998828i	$0.515413\pi$
$632$	3.12167e8	0.0491900
$633$	−9.62849e9	−1.50885
$634$	8.73745e9	1.36167
$635$	2.60673e8	0.0404006
$636$	−8.46363e8	−0.130454
$637$	2.54856e9	0.390667
$638$	−9.80137e9	−1.49422
$639$	1.82136e10	2.76148
$640$	2.30347e9	0.347338
$641$	−9.91656e9	−1.48716	−0.743580	−	0.668647i	$-0.766874\pi$
$641$	−9.91656e9	−1.48716	−0.743580	+	0.668647i	$0.766874\pi$
$642$	1.53209e10	2.28513
$643$	1.11784e10	1.65821	0.829107	−	0.559090i	$-0.188849\pi$
$643$	1.11784e10	1.65821	0.829107	+	0.559090i	$0.188849\pi$
$644$	0	0
$645$	6.65480e9	0.976509
$646$	1.47376e10	2.15086
$647$	−7.54635e8	−0.109540	−0.0547699	−	0.998499i	$-0.517443\pi$
$647$	−7.54635e8	−0.109540	−0.0547699	+	0.998499i	$0.517443\pi$
$648$	1.59226e9	0.229880
$649$	6.03425e9	0.866496
$650$	−5.43259e9	−0.775908
$651$	−1.65866e9	−0.235626
$652$	−3.38537e9	−0.478344
$653$	−9.84811e9	−1.38407	−0.692033	−	0.721866i	$-0.743285\pi$
$653$	−9.84811e9	−1.38407	−0.692033	+	0.721866i	$0.743285\pi$
$654$	1.78253e10	2.49181
$655$	9.36413e9	1.30204
$656$	4.12369e9	0.570325
$657$	−8.14364e9	−1.12031
$658$	1.36713e10	1.87076
$659$	5.14935e9	0.700896	0.350448	−	0.936582i	$-0.386029\pi$
$659$	5.14935e9	0.700896	0.350448	+	0.936582i	$0.386029\pi$
$660$	1.27710e10	1.72911
$661$	−1.13653e9	−0.153066	−0.0765328	−	0.997067i	$-0.524385\pi$
$661$	−1.13653e9	−0.153066	−0.0765328	+	0.997067i	$0.524385\pi$
$662$	1.97991e10	2.65242
$663$	1.64131e10	2.18723
$664$	−1.78990e9	−0.237269
$665$	1.03509e10	1.36490
$666$	−2.62890e10	−3.44837
$667$	0	0
$668$	−1.25340e10	−1.62695
$669$	1.17469e9	0.151682
$670$	−1.86746e10	−2.39877
$671$	828354.	0.000105849 0
$672$	−1.63549e10	−2.07901
$673$	2.35285e9	0.297537	0.148769	−	0.988872i	$-0.452469\pi$
$673$	2.35285e9	0.297537	0.148769	+	0.988872i	$0.452469\pi$
$674$	−5.54359e9	−0.697399
$675$	7.91362e9	0.990403
$676$	2.75866e9	0.343466
$677$	−2.05267e9	−0.254248	−0.127124	−	0.991887i	$-0.540575\pi$
$677$	−2.05267e9	−0.254248	−0.127124	+	0.991887i	$0.540575\pi$
$678$	−1.78730e10	−2.20238
$679$	2.58041e9	0.316333
$680$	1.53050e9	0.186660
$681$	9.51391e9	1.15437
$682$	1.41935e9	0.171334
$683$	−4.54809e9	−0.546206	−0.273103	−	0.961985i	$-0.588050\pi$
$683$	−4.54809e9	−0.546206	−0.273103	+	0.961985i	$0.588050\pi$
$684$	−2.79302e10	−3.33716
$685$	−9.19163e9	−1.09264
$686$	−1.33370e10	−1.57733
$687$	8.78635e9	1.03386
$688$	3.43553e9	0.402192
$689$	6.53740e8	0.0761444
$690$	0	0
$691$	−1.21067e8	−0.0139589	−0.00697945	−	0.999976i	$-0.502222\pi$
$691$	−1.21067e8	−0.0139589	−0.00697945	+	0.999976i	$0.502222\pi$
$692$	6.28512e9	0.721012
$693$	−1.13114e10	−1.29107
$694$	−4.98630e9	−0.566265
$695$	−1.89167e9	−0.213746
$696$	3.24401e9	0.364712
$697$	6.12202e9	0.684826
$698$	4.38537e9	0.488104
$699$	7.11509e9	0.787971
$700$	3.78596e9	0.417189
$701$	−1.61317e10	−1.76875	−0.884376	−	0.466776i	$-0.845416\pi$
$701$	−1.61317e10	−1.76875	−0.884376	+	0.466776i	$0.845416\pi$
$702$	−3.22367e10	−3.51699
$703$	1.39145e10	1.51051
$704$	7.99855e9	0.863986
$705$	−3.20003e10	−3.43948
$706$	9.24745e9	0.989021
$707$	−7.50666e8	−0.0798875
$708$	−2.20824e10	−2.33845
$709$	−5.01882e9	−0.528859	−0.264430	−	0.964405i	$-0.585184\pi$
$709$	−5.01882e9	−0.528859	−0.264430	+	0.964405i	$0.585184\pi$
$710$	−2.11376e10	−2.21641
$711$	7.15566e9	0.746631
$712$	3.65699e8	0.0379703
$713$	0	0
$714$	−2.18420e10	−2.24569
$715$	−9.86449e9	−1.00926
$716$	8.32168e9	0.847258
$717$	1.38199e8	0.0140020
$718$	−1.01192e10	−1.02026
$719$	5.38688e9	0.540488	0.270244	−	0.962792i	$-0.412896\pi$
$719$	5.38688e9	0.540488	0.270244	+	0.962792i	$0.412896\pi$
$720$	2.36313e10	2.35952
$721$	7.89785e9	0.784757
$722$	1.35761e10	1.34244
$723$	−1.63548e10	−1.60939
$724$	2.78008e9	0.272253
$725$	6.80114e9	0.662825
$726$	−1.25637e10	−1.21854
$727$	−5.69764e9	−0.549951	−0.274976	−	0.961451i	$-0.588670\pi$
$727$	−5.69764e9	−0.549951	−0.274976	+	0.961451i	$0.588670\pi$
$728$	−1.39484e9	−0.133988
$729$	−3.06669e9	−0.293172
$730$	9.45101e9	0.899183
$731$	5.10038e9	0.482938
$732$	−3.03137e6	−0.000285660 0
$733$	−4.65441e8	−0.0436517	−0.0218258	−	0.999762i	$-0.506948\pi$
$733$	−4.65441e8	−0.0436517	−0.0218258	+	0.999762i	$0.506948\pi$
$734$	−1.99224e10	−1.85954
$735$	7.93855e9	0.737455
$736$	0	0
$737$	−1.08015e10	−0.993910
$738$	−2.21551e10	−2.02898
$739$	−6.28218e9	−0.572604	−0.286302	−	0.958139i	$-0.592426\pi$
$739$	−6.28218e9	−0.572604	−0.286302	+	0.958139i	$0.592426\pi$
$740$	1.59772e10	1.44940
$741$	3.14386e10	2.83857
$742$	−8.69976e8	−0.0781796
$743$	−1.42657e10	−1.27595	−0.637973	−	0.770058i	$-0.720227\pi$
$743$	−1.42657e10	−1.27595	−0.637973	+	0.770058i	$0.720227\pi$
$744$	−4.69769e8	−0.0418195
$745$	1.26788e10	1.12339
$746$	−1.98581e10	−1.75127
$747$	−4.10292e10	−3.60140
$748$	9.78798e9	0.855141
$749$	8.24710e9	0.717158
$750$	1.92796e10	1.66872
$751$	−2.12149e9	−0.182769	−0.0913844	−	0.995816i	$-0.529129\pi$
$751$	−2.12149e9	−0.182769	−0.0913844	+	0.995816i	$0.529129\pi$
$752$	−1.65201e10	−1.41661
$753$	2.13630e10	1.82339
$754$	−2.77050e10	−2.35374
$755$	2.50940e10	2.12205
$756$	2.24657e10	1.89101
$757$	1.18334e9	0.0991457	0.0495729	−	0.998771i	$-0.484214\pi$
$757$	1.18334e9	0.0991457	0.0495729	+	0.998771i	$0.484214\pi$
$758$	1.73141e10	1.44397
$759$	0	0
$760$	2.93161e9	0.242247
$761$	−3.32564e9	−0.273545	−0.136772	−	0.990602i	$-0.543673\pi$
$761$	−3.32564e9	−0.273545	−0.136772	+	0.990602i	$0.543673\pi$
$762$	−1.05362e9	−0.0862663
$763$	9.59522e9	0.782022
$764$	9.79108e9	0.794336
$765$	3.50830e10	2.83323
$766$	−6.05221e9	−0.486535
$767$	1.70567e10	1.36493
$768$	1.73130e10	1.37914
$769$	2.21919e10	1.75975	0.879876	−	0.475203i	$-0.157626\pi$
$769$	2.21919e10	1.75975	0.879876	+	0.475203i	$0.157626\pi$
$770$	1.31273e10	1.03624
$771$	−3.79765e10	−2.98418
$772$	−5.34804e8	−0.0418344
$773$	−9.36140e9	−0.728975	−0.364487	−	0.931208i	$-0.618756\pi$
$773$	−9.36140e9	−0.728975	−0.364487	+	0.931208i	$0.618756\pi$
$774$	−1.84579e10	−1.43083
$775$	−9.84882e8	−0.0760026
$776$	7.30830e8	0.0561436
$777$	−2.06221e10	−1.57710
$778$	−1.43560e10	−1.09296
$779$	1.17265e10	0.888764
$780$	3.60991e10	2.72374
$781$	−1.22261e10	−0.918352
$782$	0	0
$783$	4.03576e10	3.00441
$784$	4.09826e9	0.303734
$785$	5.21456e9	0.384746
$786$	−3.78491e10	−2.78020
$787$	1.14447e9	0.0836937	0.0418469	−	0.999124i	$-0.486676\pi$
$787$	1.14447e9	0.0836937	0.0418469	+	0.999124i	$0.486676\pi$
$788$	−7.94176e9	−0.578196
$789$	−3.40672e10	−2.46926
$790$	−8.30441e9	−0.599258
$791$	−9.62088e9	−0.691190
$792$	−3.20365e9	−0.229143
$793$	2.34146e6	0.000166737 0
$794$	3.10094e10	2.19848
$795$	2.03635e9	0.143736
$796$	1.91829e8	0.0134809
$797$	2.51562e10	1.76012	0.880058	−	0.474867i	$-0.157504\pi$
$797$	2.51562e10	1.76012	0.880058	+	0.474867i	$0.157504\pi$
$798$	−4.18375e10	−2.91444
$799$	−2.45257e10	−1.70101
$800$	−9.71128e9	−0.670597
$801$	8.38276e9	0.576333
$802$	3.40288e10	2.32936
$803$	5.46652e9	0.372569
$804$	3.95281e10	2.68231
$805$	0	0
$806$	4.01199e9	0.269890
$807$	1.16034e9	0.0777190
$808$	−2.12606e8	−0.0141787
$809$	−1.75441e10	−1.16496	−0.582482	−	0.812844i	$-0.697918\pi$
$809$	−1.75441e10	−1.16496	−0.582482	+	0.812844i	$0.697918\pi$
$810$	−4.23581e10	−2.80052
$811$	1.03172e10	0.679183	0.339592	−	0.940573i	$-0.389711\pi$
$811$	1.03172e10	0.679183	0.339592	+	0.940573i	$0.389711\pi$
$812$	1.93075e10	1.26555
$813$	−5.40816e10	−3.52966
$814$	1.76468e10	1.14678
$815$	8.14520e9	0.527048
$816$	2.63934e10	1.70051
$817$	9.76956e9	0.626755
$818$	3.93549e10	2.51398
$819$	−3.19734e10	−2.03374
$820$	1.34648e10	0.852810
$821$	1.90058e10	1.19863	0.599316	−	0.800512i	$-0.295439\pi$
$821$	1.90058e10	1.19863	0.599316	+	0.800512i	$0.295439\pi$
$822$	3.71518e10	2.33308
$823$	−2.38126e10	−1.48904	−0.744521	−	0.667599i	$-0.767322\pi$
$823$	−2.38126e10	−1.48904	−0.744521	+	0.667599i	$0.767322\pi$
$824$	2.23685e9	0.139281
$825$	−9.78783e9	−0.606873
$826$	−2.26984e10	−1.40141
$827$	9.78569e9	0.601620	0.300810	−	0.953684i	$-0.402743\pi$
$827$	9.78569e9	0.601620	0.300810	+	0.953684i	$0.402743\pi$
$828$	0	0
$829$	−3.01748e10	−1.83951	−0.919757	−	0.392489i	$-0.871614\pi$
$829$	−3.01748e10	−1.83951	−0.919757	+	0.392489i	$0.871614\pi$
$830$	4.76159e10	2.89054
$831$	−1.30142e9	−0.0786708
$832$	2.26090e10	1.36098
$833$	6.08427e9	0.364713
$834$	7.64598e9	0.456407
$835$	3.01569e10	1.79260
$836$	1.87485e10	1.10980
$837$	−5.84424e9	−0.344500
$838$	−3.74965e10	−2.20109
$839$	−9.58551e9	−0.560336	−0.280168	−	0.959951i	$-0.590390\pi$
$839$	−9.58551e9	−0.560336	−0.280168	+	0.959951i	$0.590390\pi$
$840$	−4.34482e9	−0.252927
$841$	1.74344e10	1.01070
$842$	4.16995e10	2.40734
$843$	−4.32885e9	−0.248872
$844$	−1.62305e10	−0.929251
$845$	−6.63732e9	−0.378438
$846$	8.87566e10	5.03970
$847$	−6.76294e9	−0.382423
$848$	1.05126e9	0.0592004
$849$	−9.04503e9	−0.507263
$850$	−1.29694e10	−0.724360
$851$	0	0
$852$	4.47414e10	2.47840
$853$	−7.19448e9	−0.396897	−0.198448	−	0.980111i	$-0.563590\pi$
$853$	−7.19448e9	−0.396897	−0.198448	+	0.980111i	$0.563590\pi$
$854$	−3.11594e6	−0.000171193 0
$855$	6.72000e10	3.67695
$856$	2.33577e9	0.127283
$857$	−2.79450e10	−1.51660	−0.758301	−	0.651904i	$-0.773970\pi$
$857$	−2.79450e10	−1.51660	−0.758301	+	0.651904i	$0.773970\pi$
$858$	3.98715e10	2.15505
$859$	−8.91616e9	−0.479957	−0.239978	−	0.970778i	$-0.577140\pi$
$859$	−8.91616e9	−0.479957	−0.239978	+	0.970778i	$0.577140\pi$
$860$	1.12178e10	0.601401
$861$	−1.73794e10	−0.927946
$862$	4.53008e10	2.40897
$863$	2.01312e10	1.06618	0.533092	−	0.846057i	$-0.321030\pi$
$863$	2.01312e10	1.06618	0.533092	+	0.846057i	$0.321030\pi$
$864$	−5.76262e10	−3.03964
$865$	−1.51220e10	−0.794425
$866$	−4.37768e10	−2.29051
$867$	4.92664e9	0.256735
$868$	−2.79595e9	−0.145114
$869$	−4.80332e9	−0.248298
$870$	−8.62987e10	−4.44311
$871$	−3.05319e10	−1.56564
$872$	2.71759e9	0.138796
$873$	1.67525e10	0.852177
$874$	0	0
$875$	1.03780e10	0.523705
$876$	−2.00048e10	−1.00547
$877$	−1.09704e10	−0.549191	−0.274595	−	0.961560i	$-0.588544\pi$
$877$	−1.09704e10	−0.549191	−0.274595	+	0.961560i	$0.588544\pi$
$878$	−4.17219e10	−2.08033
$879$	−4.27116e10	−2.12122
$880$	−1.58628e10	−0.784676
$881$	−3.81338e10	−1.87886	−0.939431	−	0.342738i	$-0.888646\pi$
$881$	−3.81338e10	−1.87886	−0.939431	+	0.342738i	$0.888646\pi$
$882$	−2.20185e10	−1.08056
$883$	2.10556e10	1.02921	0.514605	−	0.857427i	$-0.327938\pi$
$883$	2.10556e10	1.02921	0.514605	+	0.857427i	$0.327938\pi$
$884$	2.76671e10	1.34704
$885$	5.31301e10	2.57655
$886$	−6.38430e8	−0.0308386
$887$	−5.78634e9	−0.278401	−0.139201	−	0.990264i	$-0.544453\pi$
$887$	−5.78634e9	−0.278401	−0.139201	+	0.990264i	$0.544453\pi$
$888$	−5.84065e9	−0.279908
$889$	−5.67155e8	−0.0270736
$890$	−9.72851e9	−0.462574
$891$	−2.45002e10	−1.16037
$892$	1.98015e9	0.0934158
$893$	−4.69779e10	−2.20757
$894$	−5.12469e10	−2.39875
$895$	−2.00219e10	−0.933524
$896$	−5.01173e9	−0.232761
$897$	0	0
$898$	−3.40203e10	−1.56773
$899$	−5.02267e9	−0.230556
$900$	2.45792e10	1.12388
$901$	1.56070e9	0.0710857
$902$	1.48719e10	0.674751
$903$	−1.44791e10	−0.654386
$904$	−2.72485e9	−0.122674
$905$	−6.68887e9	−0.299974
$906$	−1.01428e11	−4.53117
$907$	1.31715e10	0.586150	0.293075	−	0.956089i	$-0.405321\pi$
$907$	1.31715e10	0.586150	0.293075	+	0.956089i	$0.405321\pi$
$908$	1.60373e10	0.710938
$909$	−4.87347e9	−0.215211
$910$	3.71063e10	1.63231
$911$	−9.00072e9	−0.394423	−0.197212	−	0.980361i	$-0.563189\pi$
$911$	−9.00072e9	−0.394423	−0.197212	+	0.980361i	$0.563189\pi$
$912$	5.05555e10	2.20692
$913$	2.75413e10	1.19767
$914$	3.37878e10	1.46369
$915$	7.29346e6	0.000314746 0
$916$	1.48109e10	0.636718
$917$	−2.03739e10	−0.872531
$918$	−7.69599e10	−3.28334
$919$	−1.41113e10	−0.599739	−0.299869	−	0.953980i	$-0.596943\pi$
$919$	−1.41113e10	−0.599739	−0.299869	+	0.953980i	$0.596943\pi$
$920$	0	0
$921$	4.71173e10	1.98734
$922$	2.16789e9	0.0910916
$923$	−3.45588e10	−1.44661
$924$	−2.77864e10	−1.15872
$925$	−1.22451e10	−0.508704
$926$	−2.46489e10	−1.02014
$927$	5.12743e10	2.11408
$928$	−4.95253e10	−2.03427
$929$	−8.66251e9	−0.354477	−0.177239	−	0.984168i	$-0.556716\pi$
$929$	−8.66251e9	−0.354477	−0.177239	+	0.984168i	$0.556716\pi$
$930$	1.24970e10	0.509467
$931$	1.16542e10	0.473323
$932$	1.19937e10	0.485286
$933$	1.58687e10	0.639668
$934$	−3.71332e10	−1.49124
$935$	−2.35499e10	−0.942210
$936$	−9.05558e9	−0.360953
$937$	−2.24359e10	−0.890954	−0.445477	−	0.895293i	$-0.646966\pi$
$937$	−2.24359e10	−0.890954	−0.445477	+	0.895293i	$0.646966\pi$
$938$	4.06309e10	1.60748
$939$	3.52429e10	1.38913
$940$	−5.39420e10	−2.11826
$941$	−4.12869e10	−1.61528	−0.807642	−	0.589674i	$-0.799256\pi$
$941$	−4.12869e10	−1.61528	−0.807642	+	0.589674i	$0.799256\pi$
$942$	−2.10768e10	−0.821537
$943$	0	0
$944$	2.74283e10	1.06120
$945$	−5.40525e10	−2.08355
$946$	1.23901e10	0.475834
$947$	−3.68012e10	−1.40811	−0.704057	−	0.710144i	$-0.748630\pi$
$947$	−3.68012e10	−1.40811	−0.704057	+	0.710144i	$0.748630\pi$
$948$	1.75778e10	0.670092
$949$	1.54519e10	0.586881
$950$	−2.48424e10	−0.940072
$951$	4.44974e10	1.67766
$952$	−3.32996e9	−0.125086
$953$	−3.96218e10	−1.48289	−0.741445	−	0.671014i	$-0.765859\pi$
$953$	−3.96218e10	−1.48289	−0.741445	+	0.671014i	$0.765859\pi$
$954$	−5.64805e9	−0.210610
$955$	−2.35573e10	−0.875214
$956$	2.32959e8	0.00862335
$957$	−4.99157e10	−1.84096
$958$	−3.51916e9	−0.129318
$959$	1.99985e10	0.732206
$960$	7.04253e10	2.56909
$961$	−2.67853e10	−0.973563
$962$	4.98812e10	1.80644
$963$	5.35418e10	1.93197
$964$	−2.75689e10	−0.991174
$965$	1.28674e9	0.0460940
$966$	0	0
$967$	3.31992e10	1.18069	0.590343	−	0.807153i	$-0.298993\pi$
$967$	3.31992e10	1.18069	0.590343	+	0.807153i	$0.298993\pi$
$968$	−1.91542e9	−0.0678735
$969$	7.50546e10	2.64999
$970$	−1.94419e10	−0.683971
$971$	2.23646e10	0.783961	0.391981	−	0.919974i	$-0.371790\pi$
$971$	2.23646e10	0.783961	0.391981	+	0.919974i	$0.371790\pi$
$972$	2.29643e10	0.802085
$973$	4.11577e9	0.143237
$974$	3.82768e10	1.32733
$975$	−2.76667e10	−0.955964
$976$	3.76523e6	0.000129634 0
$977$	−2.31233e10	−0.793266	−0.396633	−	0.917977i	$-0.629821\pi$
$977$	−2.31233e10	−0.793266	−0.396633	+	0.917977i	$0.629821\pi$
$978$	−3.29223e10	−1.12539
$979$	−5.62703e9	−0.191664
$980$	1.33818e10	0.454175
$981$	6.22940e10	2.10671
$982$	2.21704e10	0.747108
$983$	1.42260e10	0.477691	0.238845	−	0.971058i	$-0.423231\pi$
$983$	1.42260e10	0.477691	0.238845	+	0.971058i	$0.423231\pi$
$984$	−4.92223e9	−0.164694
$985$	1.91078e10	0.637067
$986$	−6.61411e10	−2.19737
$987$	6.96242e10	2.30489
$988$	5.29952e10	1.74819
$989$	0	0
$990$	8.52252e10	2.79155
$991$	3.34542e10	1.09192	0.545962	−	0.837810i	$-0.316164\pi$
$991$	3.34542e10	1.09192	0.545962	+	0.837810i	$0.316164\pi$
$992$	7.17182e9	0.233259
$993$	1.00831e11	3.26793
$994$	4.59897e10	1.48528
$995$	−4.61541e8	−0.0148535
$996$	−1.00788e11	−3.23221
$997$	2.24944e10	0.718855	0.359427	−	0.933173i	$-0.382972\pi$
$997$	2.24944e10	0.718855	0.359427	+	0.933173i	$0.382972\pi$
$998$	5.72520e10	1.82320
$999$	−7.26616e10	−2.30582

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	529.8.a.j.1.55		65
23.5	odd	22		23.8.c.a.2.12	✓	130
23.14	odd	22		23.8.c.a.12.12	yes	130
23.22	odd	2		529.8.a.k.1.55		65

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.8.c.a.2.12	✓	130	23.5	odd	22
23.8.c.a.12.12	yes	130	23.14	odd	22
529.8.a.j.1.55		65	1.1	even	1	trivial
529.8.a.k.1.55		65	23.22	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 529 = 23^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	529.a (trivial)

\(f(q)\)	\(=\)	\(q+16.3929 q^{2} +83.4847 q^{3} +140.728 q^{4} -338.591 q^{5} +1368.56 q^{6} +736.684 q^{7} +208.646 q^{8} +4782.69 q^{9} +O(q^{10})\)	\(q+16.3929 q^{2} +83.4847 q^{3} +140.728 q^{4} -338.591 q^{5} +1368.56 q^{6} +736.684 q^{7} +208.646 q^{8} +4782.69 q^{9} -5550.49 q^{10} -3210.44 q^{11} +11748.6 q^{12} -9074.76 q^{13} +12076.4 q^{14} -28267.1 q^{15} -14592.8 q^{16} -21664.5 q^{17} +78402.2 q^{18} -41497.5 q^{19} -47649.1 q^{20} +61501.8 q^{21} -52628.5 q^{22} +17418.7 q^{24} +36518.7 q^{25} -148762. q^{26} +216700. q^{27} +103672. q^{28} +186237. q^{29} -463381. q^{30} -26969.2 q^{31} -265926. q^{32} -268022. q^{33} -355145. q^{34} -249434. q^{35} +673057. q^{36} -335309. q^{37} -680265. q^{38} -757603. q^{39} -70645.4 q^{40} -282583. q^{41} +1.00819e6 q^{42} -235425. q^{43} -451798. q^{44} -1.61937e6 q^{45} +1.13207e6 q^{47} -1.21828e6 q^{48} -280840. q^{49} +598648. q^{50} -1.80865e6 q^{51} -1.27707e6 q^{52} -72039.4 q^{53} +3.55235e6 q^{54} +1.08702e6 q^{55} +153706. q^{56} -3.46440e6 q^{57} +3.05297e6 q^{58} -1.87957e6 q^{59} -3.97797e6 q^{60} -258.019 q^{61} -442104. q^{62} +3.52333e6 q^{63} -2.49142e6 q^{64} +3.07263e6 q^{65} -4.39367e6 q^{66} +3.36449e6 q^{67} -3.04880e6 q^{68} -4.08896e6 q^{70} +3.80823e6 q^{71} +997887. q^{72} -1.70273e6 q^{73} -5.49670e6 q^{74} +3.04875e6 q^{75} -5.83985e6 q^{76} -2.36508e6 q^{77} -1.24193e7 q^{78} +1.49616e6 q^{79} +4.94100e6 q^{80} +7.63141e6 q^{81} -4.63236e6 q^{82} -8.57869e6 q^{83} +8.65501e6 q^{84} +7.33541e6 q^{85} -3.85931e6 q^{86} +1.55479e7 q^{87} -669844. q^{88} +1.75273e6 q^{89} -2.65463e7 q^{90} -6.68523e6 q^{91} -2.25152e6 q^{93} +1.85579e7 q^{94} +1.40507e7 q^{95} -2.22007e7 q^{96} +3.50274e6 q^{97} -4.60379e6 q^{98} -1.53545e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 65 q + 8 q^{2} + 14 q^{3} + 3776 q^{4} - 1181 q^{5} + 1082 q^{6} - 3628 q^{7} - 5757 q^{8} + 38263 q^{9}+O(q^{10}) \) 65 * q + 8 * q^2 + 14 * q^3 + 3776 * q^4 - 1181 * q^5 + 1082 * q^6 - 3628 * q^7 - 5757 * q^8 + 38263 * q^9	\( 65 q + 8 q^{2} + 14 q^{3} + 3776 q^{4} - 1181 q^{5} + 1082 q^{6} - 3628 q^{7} - 5757 q^{8} + 38263 q^{9} - 6879 q^{10} - 26147 q^{11} + 35689 q^{12} - 100 q^{13} - 55020 q^{14} - 92935 q^{15} + 176888 q^{16} - 89552 q^{17} + 190670 q^{18} - 169530 q^{19} - 210098 q^{20} - 190951 q^{21} - 218663 q^{22} + 190835 q^{24} + 721210 q^{25} + 186894 q^{26} - 670321 q^{27} - 366019 q^{28} + 340963 q^{29} - 671873 q^{30} - 175163 q^{31} - 406068 q^{32} - 726837 q^{33} - 1110895 q^{34} - 596883 q^{35} + 361164 q^{36} - 790283 q^{37} - 1963838 q^{38} - 21993 q^{39} - 1600645 q^{40} - 623859 q^{41} - 2696872 q^{42} - 1189188 q^{43} - 3885217 q^{44} - 2158369 q^{45} + 1365507 q^{47} + 1218748 q^{48} + 5854235 q^{49} - 2728396 q^{50} - 4554663 q^{51} + 7887791 q^{52} - 4362562 q^{53} + 5072916 q^{54} - 3989544 q^{55} - 12949007 q^{56} - 551326 q^{57} - 7443768 q^{58} + 13201460 q^{59} - 19296285 q^{60} - 8838644 q^{61} - 14615728 q^{62} - 12479203 q^{63} - 9711751 q^{64} - 13544545 q^{65} - 4907285 q^{66} - 5760553 q^{67} - 17044359 q^{68} + 6122411 q^{70} + 4531745 q^{71} + 10759455 q^{72} - 2535486 q^{73} - 21404597 q^{74} + 22917428 q^{75} - 21958812 q^{76} + 11733492 q^{77} - 35437508 q^{78} - 27234683 q^{79} - 28932289 q^{80} + 3995985 q^{81} - 11682773 q^{82} - 39797339 q^{83} - 33971997 q^{84} - 19766357 q^{85} - 43836707 q^{86} - 13972389 q^{87} - 33099818 q^{88} - 41235321 q^{89} - 17210275 q^{90} - 30292506 q^{91} + 47965734 q^{93} - 9981701 q^{94} - 5998448 q^{95} - 48738628 q^{96} - 13984256 q^{97} + 56728191 q^{98} - 81303822 q^{99}+O(q^{100}) \) 65 * q + 8 * q^2 + 14 * q^3 + 3776 * q^4 - 1181 * q^5 + 1082 * q^6 - 3628 * q^7 - 5757 * q^8 + 38263 * q^9 - 6879 * q^10 - 26147 * q^11 + 35689 * q^12 - 100 * q^13 - 55020 * q^14 - 92935 * q^15 + 176888 * q^16 - 89552 * q^17 + 190670 * q^18 - 169530 * q^19 - 210098 * q^20 - 190951 * q^21 - 218663 * q^22 + 190835 * q^24 + 721210 * q^25 + 186894 * q^26 - 670321 * q^27 - 366019 * q^28 + 340963 * q^29 - 671873 * q^30 - 175163 * q^31 - 406068 * q^32 - 726837 * q^33 - 1110895 * q^34 - 596883 * q^35 + 361164 * q^36 - 790283 * q^37 - 1963838 * q^38 - 21993 * q^39 - 1600645 * q^40 - 623859 * q^41 - 2696872 * q^42 - 1189188 * q^43 - 3885217 * q^44 - 2158369 * q^45 + 1365507 * q^47 + 1218748 * q^48 + 5854235 * q^49 - 2728396 * q^50 - 4554663 * q^51 + 7887791 * q^52 - 4362562 * q^53 + 5072916 * q^54 - 3989544 * q^55 - 12949007 * q^56 - 551326 * q^57 - 7443768 * q^58 + 13201460 * q^59 - 19296285 * q^60 - 8838644 * q^61 - 14615728 * q^62 - 12479203 * q^63 - 9711751 * q^64 - 13544545 * q^65 - 4907285 * q^66 - 5760553 * q^67 - 17044359 * q^68 + 6122411 * q^70 + 4531745 * q^71 + 10759455 * q^72 - 2535486 * q^73 - 21404597 * q^74 + 22917428 * q^75 - 21958812 * q^76 + 11733492 * q^77 - 35437508 * q^78 - 27234683 * q^79 - 28932289 * q^80 + 3995985 * q^81 - 11682773 * q^82 - 39797339 * q^83 - 33971997 * q^84 - 19766357 * q^85 - 43836707 * q^86 - 13972389 * q^87 - 33099818 * q^88 - 41235321 * q^89 - 17210275 * q^90 - 30292506 * q^91 + 47965734 * q^93 - 9981701 * q^94 - 5998448 * q^95 - 48738628 * q^96 - 13984256 * q^97 + 56728191 * q^98 - 81303822 * q^99

Introduction

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